API: Inconsistent use of `apply` arguments args and **kwargs

[datapythonista]

The signature of Series.apply (and DataFrame.apply) seems inconsistent and cumbersome (see args and **kwargs:

Series.apply(func, convert_dtype=True, args=(), **kwargs)

I'd expect to have args and kwargs, or *args and **kwargs, not a mix of both. I assume this was implemented to allow convert_dtype to be passed as a positonal argument:

my_series.apply(my_func, this_is_convert_dtype)

But this seems confusing and not very intuitive:

my_series.apply(my_func, this_arg_is_for_apply, this_must_be_a_tuple_with_all_args, this_is_a_single_kwarg=True, this_is_another_kwarg=False)

To me, the API would be much clear if it was implemented as:

Series.apply(func, *, convert_dtype=True, args=(), kwargs={})

# or

Series.apply(func, convert_dtype=True, *, args=(), kwargs={})

And I think this can be easily done in two steps, warning the user first without breaking code. If there is agreement, I'd also do the same for the rest of the methods using this same pattern.

[attack68]

link for relevancy #39987

[rhshadrach]

I think this is a duplicate of #40112

Edit: on second reading, it is a bit different, but should be taken into consideration in that issue.